Differential time domain spectroscopy method for measuring thin film dielectric properties

Abstract

A non-contact, free-space method for determining the index of refraction of a thin film at a desired angular frequency. The method includes generating an input desired-frequency pulse and an optically detectable probe pulse. The thin film is moved in and out of the path of the input pulse, creating an output pulse that alternates between a transmitted signal, created when the film intercepts the input pulse path, and a reference signal, created when the sample is outside the input pulse path. The output pulse modulates the probe pulse, which is then detected with a photo detector, and the difference between the transmitted signal and the reference signal is calculated. The above steps are repeated over a plurality of delay times between the input pulse and the probe pulse until a complete field waveform of the differential signal is characterized. The index of refraction is calculated as a function of a ratio between the differential signal for the thin film and the reference signal. A complete field waveform of the reference signal may be characterized by repeating the above steps for a reference plate identical to the sample except having a non-transmissive film instead of the thin, transmissive film.

What is claimed:  
     
       1. A non-contact method for determining in a free space the index of refraction (n 2 (ω) at a desired angular frequency (ω) of a sample including a thin, transmissive film having a thickness (d) and optionally disposed on a substrate, the method comprising: 
       (a) generating (i) an input desired-frequency pulse having a first wavelength and a first duration, and (ii) a probe pulse having a second wavelength shorter than the first wavelength and a second duration shorter than the first duration;  
       (b) directing the input pulse along a first path and the probe pulse along a second path;  
       (c) moving the sample in and out of the first path, creating an output pulse which alternates between a transmitted signal (E film (ω)), created when the sample is in the first path, and a reference signal (E ref (ω)), created when the sample is outside the first path;  
       (d) modulating the probe pulse by the output pulse;  
       (e) detecting the modulated probe pulse with a photo detector;  
       (f) calculating a differential signal (E diff (ω)) for the thin film comprising a difference between the transmitted signal and the reference signal;  
       (g) repeating steps (a)-(f) over a plurality of delay times between the input pulse and the probe pulse until a complete field waveform of the differential signal for the thin film is characterized; and  
       (h) calculating the index of refraction as a function of a ratio between the differential signal for the thin film and the reference signal.  
     
     
       2. The method of  claim 1  further comprising, between steps (g) and (h), characterizing a complete field waveform of the reference signal by repeating steps (a)-(g) for a reference plate identical to the sample except comprising a non-transmissive film instead of the thin, transmissive film, the non-transmissive film mounted on an optional substrate identical to the sample optional substrate when present in the sample, such that in step (c) for the reference plate, the output pulse alternates between the reference signal (E ref (ω)), created when the non-transmissive film is outside the first path, and an absence of a signal, created when the non-transmissive film blocks the first path, such that in steps (f) and (g) for the reference plate, the differential signal for the non-transmissive film is equal to the reference signal. 
     
     
       3. The method of  claim 1  wherein the function for the index of refraction comprises: 
       
         
             n   2 (ω)={square root over (( n   1   +n   3 )(1 +A (ω))− n   1   n   3 )} 
         
       
       where:          A        (   ω   )       =       c     ω                 d                     E   diff          (   ω   )           E   ref          (   ω   )                                
       n 1 =index of refraction of the free space, and  
       n 3 =index of refraction of the optional substrate.  
     
     
       4. The method of  claim 1  wherein the desired-frequency pulse has a gigahertz to terahertz frequency. 
     
     
       5. The method of  claim 4  wherein the desired-frequency pulse has frequency less than about 10 gigahertz. 
     
     
       6. The method of  claim 1  wherein the probe pulse is optically detectable. 
     
     
       7. The method of  claim 1  further comprising determining a dielectric constant for the thin film by calculating the index of refraction squared. 
     
     
       8. The method of  claim 1  wherein: 
       step (a) comprises creating a first laser pulse and a second laser pulse, the first laser pulse being an excitation pulse that travels through a variable-length delay stage and impinges upon an emitter that becomes excited and emits the desired-frequency input pulse;  
       step (c) comprises moving the thin film in and out of the first path using a galvanometer;  
       step (d) comprises modulating the probe pulse by the output pulse using an electro-optical sensor to create an electro-optical resultant having a linear polarization;  
       between steps (d) and (e), the method further comprises circularly polarizing the electro-optical resultant with a quarter waveplate and linearly polarizing the circularly polarized electro-optical resultant in a prism which splits the resultant into a first detectable pulse and a second detectable pulse;  
       step (e) comprises detecting the first detectable pulse with a first photo detector and the second detectable pulse with a second photo detector and sending the pulses through circuitry which outputs noise-reduced electronic information;  
       step (f) comprises receiving the electronic information in a lock-in amplifier synchronized with the galvanometer to output electronic information corresponding to the differential signal;  
       step (g) comprises characterizing the complete waveform of the reference signal and the differential signal as time-domain signals, and  
       step (h) comprises calculating a Fourier transform of the complete time domain waveforms of the reference signal and the differential signal to provide complete frequency-domain signals for use in calculating the index of refraction.  
     
     
       9. The method of  claim 8  comprising directing a source laser pulse through a polarizer and a polarization beam splitter to produce the first pulse and the second pulse. 
     
     
       10. The method of  claim 1  wherein the thin film has a thickness less than 2 μm.